Morningstar® yet again paints a gloomy picture of the so-called “average investor returns.” The thesis is that these returns are generally lower than mutual fund returns because of investors’ poor timing: they make contributions before market downturns and withdrawals before rebounds, similarly to what they do with ETFs. Morningstar’s annual findings have been subsequently propagated by articles in The New York Times and MarketWatch.

To calculate the investor return, Morningstar takes into account the initial value of the fund’s assets, all inflows and outflows for the fund, and the end asset value, all obtained from the fund’s filings in a given period. This calculation is similar to that of the internal rate of return (IRR).

However, there is one major issue with this methodology: the IRR calculated from the fund’s aggregate cash flows is not the same as the average of IRRs realized by all investors in the fund. To determine the latter, Morningstar would have to take a representative sample of investors in the fund, calculate their individual IRRs, and then take an average of those IRRs.

Such a representative sample would need to have at least 20-30 investors, which, if multiplied by over 23,000 funds (all separate share classes), and applied on a regular basis, would be impractical. Hence the convenient shortcut of using only the overall cash flows of the fund and attributing the resulting IRR to a “typical investor.”

This approach not only results in inaccurate figures but also assumes that there exists such a hypothetical average investor whose cash flows into and out of the fund precisely mimicked (in proportion) the composite cash flows of the fund. As Alpholio™ stated in previous posts, it is highly unlikely that such an investor exists.

To illustrate the point, Alpholio™ constructed a simple Microsoft® Excel® simulation of a mutual fund (spreadsheet is available upon request). The simulation spans a period of 12 months and assumes that the fund had 30 investors; in this case, the sample size is the entire population. The simulation has six parameters governing its outcomes (all random variables have normal distributions):

The amount and standard deviation of the initial investment in the fund. For example, $10,000 and 10%, meaning that 99.7% of the investors initially invested between $7,000 and $13,000 in the fund.

The annualized return and standard deviation of return of the fund. For example, 10% and 15%, respectively, which models the typical attributes of the S&P 500® index.

Inflow/outflow base amount and corresponding standard deviation. For example, $10,000 and 10%. This results in random contributions to and withdrawals from the fund each investor would make monthly. (The limit, of course, is that an investor cannot withdraw more than he/she has left in the fund.)

All initial investments are assumed to be made at the end of the month preceding the start of the simulation (e.g. December 31, 2012). All additional contributions to and withdrawals from the fund are assumed to be made on the first day of each month (e.g. from January to December 2013). The return of the fund randomly varies monthly. The spreadsheet can be recalculated by pressing the F9 key, upon which a new series of random scenarios is generated and charted.

The simulation calculates individual IRRs of all 30 investors based on each investor’s random cash flows. It also calculates the overall IRR based on the aggregate cash flows of the fund. The difference between the latter and the former is the IRR error.

It turns out that across many simulation runs, the the average IRR error is relatively small, i.e. around +0.1%. This means that, on average, the fund flow IRR overestimates the true average investor IRR by that small amount. However, the standard deviation of the error is relatively large, i.e. about 0.6%. This means that the error is typically distributed in the -1.7% to +1.9% range. This puts into question the accuracy of 10-year “return gaps” cited by Morningstar in the negative 1.66% to 3.14% range for various mutual fund categories.

Here is a sample distribution of the error in 1000 simulations:

While the interpolation line is somewhat jagged, a normal-like distribution shape clearly emerges.

In conclusion, while this simple simulation is by no means perfect or exhaustive, it does demonstrate that the calculation of a “typical investor return” based solely on the composite flows of the fund can be quite inaccurate. Due to the non-linear, iterative nature of the IRR calculation, the IRR of the aggregate cash flows is not the same as the average IRR of individual investor cash flows. Hence, both investors and the media should interpret the “average investor return” figures with caution.

An article in The Wall Street Journal claims that many investors earn lower returns than their investments do. This is caused by buying and selling mutual fund shares at a wrong time. The author cites an example of the PIMCO Total Return Fund:

In the year ended Sept. 30, its largest share class lost 0.74% — a respectable result, considering that the bond benchmark the fund seeks to beat, the Barclays U.S. Aggregate index, lost 1.89%.
…
According to people familiar with the fund, its investors incurred an average loss of 1.4% over this period, nearly double the loss of the fund itself. That is because investors bought high and sold low, locking in the fund’s interim losses and missing its later gains.

First, the largest share class of the fund, returning -0.74% in one year to September 30, is institutional (PTTRX). This share class requires a minimum initial investment of $1 million, which is impractical for most individual investors. Therefore, for further analysis this post will use the class A shares (PTTAX) with a minimum initial investment of $1,000.

Second, the problem with this assessment is that it is solely based on the general cash inflows and outflows of the fund, and not the analysis of circumstances of individual investors. This subject was already covered in a previous Alpholio™ post, which found a problem with

…a notion that there exists an “average investor” whose investments into and withdrawals from the fund precisely mimicked the inflows and outflows generated by all of the fund’s investors in both time and relative scale (for one, there is no proof that these same investors who cashed out later reinvested into the fund).

To illustrate that point, let’s analyze a situation of a hypothetical market timing investor who invested into PTTAX on September 28, 2012 (the last trading day of that month) and did not pay the front load of the fund. In May 2013, the investor was observing rising interest rates, which caused the NAV of the fund to fall, and decided to terminate the investment on May 31, 2013, i.e. in the middle of the May/June massive withdrawal period quoted by the article. According to Morningstar’s “growth of $10,000” figures, which assume reinvestment of all fund distributions, the investor realized a return of +0.502% in that period. Had the investor instead retained the investment in the fund until September 30, 2013, the total return would have been -1.128%. This clearly shows why doing an “average investor” return calculation solely based on fund inflows and outflows is misleading.

Furthermore, the above scenario does not take into account what the investor did with the proceeds from the May 31 sale. If the investor kept the proceeds in a money market fund with a typical annual yield of a few basis points, then the return through September 30 would be only slightly higher than the +0.502% calculated above. However, the investor certainly had many other investment possibilities, both in fixed income and in equities.

For example, let’s assume that in the face of rising rates (the duration of PTTAX is approx. five years) the fixed-income investor decided to invest the proceeds in a short-term taxable bond fund, such as the PIMCO Short-Term Fund (PSHAX, class A shares), again without paying a front load. From June 3, 2013 to September 30, 2013, the total return of PSHAX was -0.057%. Therefore, this hypothetical market-timing investor would have realized a total return of (1 + 0.502%) x (1 – 0.057%) – 1 = +0.445%, still better than the -1.128% for PTTAX alone. This again illustrates that estimating fund investors’ returns without taking into account follow-up investments (into which an analyst may not have visibility) is misguided.

In sum, while a buy-and-hold strategy can certainly produce good long-term results for most investors, in a case of prolonged rock-bottom interest rates, some market timing may be warranted.

An article in InvestmentNews discusses how “average investors” in some of the top ten large-cap mutual funds failed to beat the market over a recent five-year period due to market timing:

Over the five-year period ended Aug. 31, which includes the collapse of Lehman Brothers Holdings Inc. in 2008, the S&P 500’s 42% free fall to the bear market’s bottom and its subsequent 130% rally, five of the 10 biggest large-cap-stock funds posted better annualized returns than the benchmark.

The average investor return, which takes into account buying and selling behavior, for all but one of the funds was much lower because investors were busy selling, according to Morningstar Inc.
Only investors in the T. Rowe Price Growth Fund enjoyed the full market cycle’s outperformance. The average investor return over the past five years in the fund was 8.85%, beating the fund’s 8.63% return.

So, what’s wrong with the article’s thesis? First, a simplified proposition of looking at just the fund’s returns without taking the fund’s risk into account. Second, the use of a single performance benchmark (the S&P 500® index, a proxy for “the market”) that cannot fully adjust for that risk. Third, a notion that there exists an “average investor” whose investments into and withdrawals from the fund precisely mimicked the inflows and outflows generated by all of the fund’s investors in both time and relative scale (for one, there is no proof that these same investors who cashed out later reinvested into the fund). Fourth, a surprising indication that market timing may actually work in some cases (e.g. PRGFX). Fifth, looking at just one specific time period for a very small number of funds to derive the following speculation:

After all, five years from now, it may be funds such as the American Funds Growth Fund of America (AGTHX) or the American Funds Investment Co. of America Fund (AIVSX) that are sporting the best 10-year annualized returns, even though both have underperformed these past five years.

How would a truly risk-adjusted performance of the five funds look like over an extended period of time, which includes the interval used in the article? Here is one example, as a continuation of a previous Alpholio post on Fidelity® Contrafund®:

The chart clearly shows that on a cumulative RealAlpha™ basis, the fund started to underperform its reference portfolio in late 2007, i.e. well before the onset of the financial crisis. Therefore, the following five-year period was largely irrelevant to those investors who practiced “market timing” based on the above information.